Math

Rørdam K-theory

2.2.10 Liftings

Chapter 2 Projections and Unitary elements

Chapter 3 The K_0 Group of a Unital C -algebra.

Chapter 4 The functor K0

Chapter 5 The ordered abelian group K0

Chapter 6 Inductive limits

Characterization for stable equivalence

Corollary 2.1.4

Definition 2.1.2.

Definition 2.2.1

Definition 2.3.1 (The semigroup of projections of A)

Definition 2.3.3. (The semigroup of projections)

Definition 3.1.4 (The K_0 group of a Unital C-algebra)

Definition 3.1.6 (Stable equivalence)

Definition 3.2.5 (Homotopy equivalence)

Definition 4.1.1 (K0, non-unital case)

Definition 4.2.1 (The Scalar mapping)

Definition 5.1.1.

Definition 5.1.3

Definition 5.1.4 (Positive cone of K0)

Definition 5.16

Definition 6.4.a (Stabilization)

Drawing 2024-02-05 22.07.46

Lemma 2.1.5 (Whitehead)

Murray-von Neumann equivalence

Paragraph 3.3.1 Traces and K0

Properties of the Grothendieck group

Proposition 2.1.6.

Proposition 2.1.8

Proposition 2.1.11

Proposition 2.2.5

Proposition 2.2.6

Proposition 2.2.7

Proposition 2.2.8

Proposition 2.3.2.

Proposition 3.1.7 (The standard picture for K0 — the unital case)

Proposition 3.1.8 (Universal property of K0)

Proposition 3.2.4 (Functoriality of K0 for unital C-star Algebras)

Proposition 3.2.6 (Homotopy invariance of K0)

Proposition 4.1.3 (Functoriality of K0)

Proposition 4.1.4 (Homotopy invariance of K0)

Proposition 4.3.2 (Half exactness of K0)

Proposition 4.3.3 (Split exactness of K0)

Proposition 4.3.4 (Direct sums)

Proposition 4.3.8 (Stability)

Proposition 5.1.5

Proposition 5.1.7

Proposition 5.1.9.

Proposition 6.2.4

Proposition 6.4.1 (Stability of K0)

Rørdam K-theory

The functor K00 3.2.3

The functor K0 for unital C-star Algebras 3.2.2

The Grothendieck construction 3.1.1

The group K_00 3.1.5

Theorem 2.1.9. (The polar decomposition)

Theorem 2.1.10 (Carl Neumann Series)

Theorem 4.1.2. (The functor K0)

Theorem 6.3.2 (Continuity of K0)

Diffuse measure

finite C-star algebra

finite projection

infinite C-star algebra

infinite projection

probability measure

quasi-trace

A quasi-trace on a -algebra , is a continuous , that satisfies for all and . For all commuting elements in
.
A theorem of Haagerup gives that every quasi-trace on an exact C-star algebra unital -algebra extends to a trace.

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